Solving for Angular Frequency of 2 Masses on a Spring

In summary, angular frequency is a measure of how quickly an object moves in a circular path, measured in radians per second (rad/s). It is related to the frequency of motion by the equation ω = 2πf, where ω is the angular frequency and f is the frequency in hertz (Hz). The angular frequency of a mass-spring system is directly proportional to the square root of the spring constant and inversely proportional to the square root of the mass. To solve for the angular frequency of a system with two masses on a spring, you can use the equation ω = √(k/m) and substitute in the values for the spring constant and the combined mass of the two masses. The period of an
  • #1
usamo42j
10
0

Homework Statement


Two identical objects of mass m are placed at either end of a spring of spring constant k and the whole system is placed on a horizontal frictionless surface. At what angular frequency ω does the system oscillate?


Homework Equations


ω=√(k/m)


The Attempt at a Solution



Total mass is 2m, so ω=√(k/2m)

Apparently that's not right, though my answer does not really seem reasonable, as it should be oscillating faster than with one mass...?
 
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  • #2
Hi usamo,

Write out Newton's second law for both bodies.

ehild
 

FAQ: Solving for Angular Frequency of 2 Masses on a Spring

What is angular frequency?

Angular frequency is a measure of how quickly an object moves in a circular path. It is measured in radians per second (rad/s) and is related to the frequency of motion by the equation ω = 2πf, where ω is the angular frequency and f is the frequency in hertz (Hz).

How is angular frequency related to mass and spring constant?

The angular frequency of a mass-spring system is directly proportional to the square root of the spring constant and inversely proportional to the square root of the mass. This can be expressed as ω = √(k/m), where k is the spring constant and m is the mass.

How do you solve for the angular frequency of two masses on a spring?

To solve for the angular frequency of a system with two masses on a spring, you will need to use the equation ω = √(k/m) and substitute in the values for the spring constant and the combined mass of the two masses. If the masses are unequal, you will also need to use the reduced mass formula, which takes into account the relative mass distribution of the two masses.

What is the relationship between angular frequency and period?

The period of an object in circular motion is the time it takes for one complete revolution. It is related to the angular frequency by the equation T = 2π/ω, where T is the period and ω is the angular frequency. This means that as the angular frequency increases, the period decreases and vice versa.

Can angular frequency be negative?

Yes, angular frequency can be negative. This indicates that the object is rotating in the opposite direction from what is considered positive. However, in most cases, the magnitude of the angular frequency is more important than its direction, so the negative sign is often dropped. In mathematical calculations, it is important to keep track of the sign to ensure accurate results.

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